Oscillation of some ordinary differential equations and difference equations (Q2706020)

Some ordinary differential equations, functional-differential equations and difference equations as well as systems formed by them are considered. The oscillatory properties of these equations and systems are compared. It is shown that the systems can be reduced to integro-differential equations by a proper transform and then it is proved that a finite number of zeros of the solutions exists. The same is proved for systems of difference equations with solutions changing their signs finite number of times. Some properties of nonoscillatory and oscillatory solutions are investigated. Oscillation, boundedness and monotonicity criteria are discussed. The author presents interesting statements concerning the existence of nonoscillatory bounded solutions and some comparison theorems.